Web apps are the same as desktop apps in terms of how you should develop them:
Step 1) Write the functional spec of what it is you want. Since this is a new development arena for you, I recommend an iterative project development method such as Agile .
Step 2) Create a basic design from your spec. The first iteration is/should be language/platform independent. Identify where (user input) requests will come from, what (general) component will handle the requests and directing the appropriate component to handle them.
Step 3) Look at a few technologies. See what components/features they have that will match up with the needs of your application.
Step 4) Choose the language/framework and write the very most basic piece of it that you can to demonstrate a working app. For instance, a login and username display page. This could be for instance installing Drupal, and echoing data out of a custom table on the login /welcome page.
Step 5) See if you already want to tear your hair out and poke out your own eyes. If you do at this point, go back to step 4 and do it over with something else. Each of these step 4-5 iterations should take no more than 2-3 days. Even if your very first app doesn't make you want to kill yourself, you may want to give another 2-3 day window to try one more app just to confirm you have the right stuff.
Step 6) Stick with your choice and write a few additional small components. If you find you want to kill yourself in the first 2 weeks, you should identify on paper what the shortcomings specifically are and see if you can write a library for that stuff, or give one last shot to choosing another framework.
Step 7) Suck it up and build the app. Hopefully you can release the components AND documentation open source for the libraries you used to make your life liveable while building the app and save us all a lot of time as well.